Evaluate the exponent using the power to a power rule.
(3^3)^7

The system of equations which is represented the equivalent single equation without the y variable in it is x-1=0.

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The system of equations as an equivalent single equation without the y variable has to be found out for the given equation.

The first equation given in the problem is,

\(x + y = 10\)

Subtract x from both sides and solve it for y,

\(x + y -x= 10-x\\y=10-x\)                    .........1

The second equation given in the problem is,

\(y = 4x + 5\)

Put the value of y in this equation from equation 1 as,

\(y = 4x + 5\\10-x = 4x + 5\\10-5=4x+x\\5=5x\\5x-5=0\)

Divide both side with number 5,

\(x-1=0\)

Thus, the system of equations which is represented the equivalent single equation without the y variable in it is x-1=0.

Learn more about the system of equations here;

https://brainly.com/question/13729904

#SPJ1

The sunflower would be 30 inches tall after 30 weeks. The sunflower be after w weeks would be 25 + 0.5 * w inches tall.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

To calculate the height of the sunflower after 10 weeks, we can use the formula:

=>height = starting height + growth rate * time elapsed

where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.

So the height after 10 weeks would be:

=>height = 25 + 0.5 * 10 = 25 + 5 = 30 inches

Therefore, the sunflower would be 30 inches tall after 10 weeks.

To calculate the height after w weeks, we can use the same formula:

=>height = 25 + 0.5 * w

So the height after w weeks would be:

=>height = 25 + 0.5 * w inches

To learn more about expression refer the below link

https://brainly.com/question/112703

#SPJ1

The truth table for the statement is

r     s     ¬r    s ∧ ¬r

---------------------

T     T     F     F  

T     F     F     F  

F     T     T     T

F     F     T     F

From the question, we have the following parameters that can be used in our computation:

s ∧ ¬r

To construct the truth table, we make use of the following notations

s, r and ¬r

The truth table for the statement s ∧ ¬r is then represented as follows:

r     s     ¬r    s ∧ ¬r

---------------------

T     T     F     F  

T     F     F     F  

F     T     T     T

F     F     T     F

The condition for ∧ is that it is true if both statements are true

Read more about truth table at

brainly.com/question/14458200

#SPJ1

Answer:

The constraints are:

Plot the graphs of the constraints

From the graph (see attachment), the only optimal point is (3,4)

Substitute 3 for x and 4 for y in the objective function.

So, we have:

Hence, the maximum value of C is 17

Step-by-step explanation: Hope this helps!!!

Answer:

In other words, 740 is 22% of "some number."

"per cent" means "out of 100." So...

Set up a proportion: 22/100 = 740/n

Cross-multiply so that 22n = 74,000

Then divide both sides by 22 to get...

n = 3363.6, but since you can't have .6 of a person, round up to 3364.

Hope this helps!

Answer:

hey, im sorry to hear that. evreyone (mostly) is going through the same thing... teachers are uploading loads of work. and understand that it may be stressful... they have to understand us students are also dealing with our own problems. so please take ur time to develop a good mindset! ily and im  Proud of you for evreything you have accomplished… ur teacher may have not taught you alot but im here to help u and so is everyone in brainly! You can do this! You can make it! Its gonna  be okay and i understand  u may have alot of stuff on ur mind and not just school. 2020 has been a mess and i hope 2021 is better not just for u but for all of us… i really hope u get through this and i will try my best to help u and so will everyone on here! Ur gonna do great luv! Just keep ur head up<3 i love u and im so proud of u for making it this far! Its gonna be okay. It will all fade and everything will be back to normal someday! <333

Based on the market research, Dina can determine which ice cream flavor she should put on sale this week by comparing the number of people who would purchase each flavor if it was on sale.

For example, if 70 people said they would purchase chocolate ice cream if it was on sale and only 30 people said they would purchase vanilla ice cream if it was on sale, then Dina should put chocolate ice cream on sale this week.

On the other hand, if 60 people said they would purchase vanilla ice cream if it was on sale and only 40 people said they would purchase chocolate ice cream if it was on sale, then Dina should put vanilla ice cream on sale this week.

It's important to note that Dina's market research only represents a sample of people who walk by her ice cream shop and stop in. It may not be representative of the entire population of potential customers. Therefore, Dina should take this into account when making her decision.

Read more about market research here:

https://brainly.com/question/24906199

#SPJ1

When he sells 200 hamburgers, the AVC is $13.5.

The average cost curve starts to rise when there are 250 hamburgers produced.

Given info,

Slider is the proprietor of a burger joint. For a quantity of 100 hamburgers, the slider's minimal average variable cost is $10, and for a quantity of 200 hamburgers, his minimum average total cost is $15. He has a $300 total fixed cost. Use his knowledge to respond to the questions.

Let,

Minimum average variable cost (AVC) = $10, when Q = 1 in00 hamburgers Minimum average cost (AC) = $15, when Q = 200 hamburgers

Fixed cost = $300

To compute the AVC when Q = 200 hamburgers, first compute Total cost (TC) as follows,

TC = AC * Q

     = 15 * 200

     = 3,000

Now, subtract fixed cost from TC that results variable cost (VC) as follows;

VC = TC - fixed cost

     = 3,000 - 300

     = 2,700

Now, compute the AVC when Q = 200 hamburgers as follows,

AVC = VC / Q

        = 2,700 / 200

        = 13.5

Hence, the AVC when he sells 200 hamburgers is $13.5

At a quantity of 250 hamburgers, the average cost curve is increasing.

To learn more about average click here:

brainly.com/question/24057012

#SPJ4

Answer:

21

Step-by-step explanation:

Except than x = 1, all real numbers fall within the function's domain.

Since there are no limitations on what we can substitute for x, the domain of a function, f(x), is all real numbers because any real numbers would make f(x) a defined function. As a result, when this is not the case, the domain of a function, f(x), is not all real numbers.

The rational function r(x) = 2x/(x-1) is defined as follows.

So, we set the denominator to zero and solve for x in order to determine the domain of r(x):

x - 1 = 0

x = 1

Hence, x = 1 is the only value of x that causes the denominator to equal 0. R(x) therefore has a domain of all real numbers other than x = 1.

We can express the domain as follows in interval notation:

(-∞, 1) U (1, ∞)

Except than x = 1, all real numbers fall within the function's domain.

To know more about function visit:-

https://brainly.com/question/14830166

#SPJ1

Question:

Which of the following correctly describes the domain of the function shown below?

r(x) = 2x x-1

A. {x:x0}

B. {x: x = 1}

c. x all .real .numbers}

D. xx1}

Answer:

  (d)  1/5^7

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)/(a^c) = 1/(a^(c-b))

__

  \(\dfrac{5^{-4}}{5^3}=\dfrac{1}{5^{3-(-4)}}=\boxed{\dfrac{1}{5^7}}\)

Answer:

-8

Step-by-step explanation:

Variable k is denoted for vertical movement of a graph. In this case, -8 is k. The graph is moving down 8 units from the parent graph.

The given polynomial, 6•x² + 12•x + 6, can be factored by rearranging and looking for the common factors to give;

6•x² + 12•x + 6 = 6•(x + 1)²

The given polynomial is presented as follows;

6•x² + 12•x + 6

The coefficients in the terms and the constant have a common factor of 6, which gives;

6•x² + 12•x + 6 = 6•(x² + 2•x + 1)

x² + 2•x + 1 = x² + x + x + 1

x² + x + x + 1 = x•(x + 1) + 1•(x + 1)

x•(x + 1) + 1•(x + 1) = (x + 1)•(x + 1) = (x + 1)²

Therefore;

x² + 2•x + 1 = (x + 1)²

6•(x² + 2•x + 1) = 6•(x + 1)²

6•x² + 12•x + 6 = 6•(x² + 2•x + 1)

Therefore;

Learn more about how to factoring a polynomial here:

https://brainly.com/question/24351176

#SPJ1

Answer:

20 units

Step-by-step explanation:

Let the length be x. According to the question,

➝ Width = 15% of the length

➝ Width = 15/100x

➝ Width = 3/20x

We have the perimeter of the rectangle that is 46 units.

\(\longrightarrow \sf {Perimeter_{(Rec.)} = 2(L + W) } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{20x + 3x}{20} \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{23x}{20} \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {\dfrac{46}{2}= \dfrac{23x}{20}} \\ \)

\(\longrightarrow \sf {23= \dfrac{23x}{20}} \\ \)

\(\longrightarrow \sf {23 \times 20 = 23x} \\ \)

\(\longrightarrow \sf {460= 23x} \\ \)

\(\longrightarrow \sf {\cancel{\dfrac{460}{23}} = x} \\ \)

\(\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\ \)

Therefore, length of the rectangle is 20 units.

Answer:

(0,1)

Step-by-step explanation:

Answer:

I think (-2,3) is

the answer

9514 1404 393

Answer:

  w + 2 = 18

Step-by-step explanation:

If w represent the number of wins, then the total number of matches is ...

  w + 2 = 18

The differential equation to be solved is Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx. This can be solved using Euler's method in MATLAB.

Follow the steps below.

Step 1: Create a function file - The differential equation needs to be defined in a function file first. Let's create a function file named "odefun.m".function dydx = odefun(x,y)

dydx = N*x*y - 0.5*y*exp(-0.1*x);

where N is a constant value that needs to be defined.

Step 2: Define the given values - Define the given values such as N, initial value y(0), and step size dx.

N = ...; %

Define N herey 0 = 6.5; %

Define initial value of y here. dx = ...; %

Define step size here

Step 3: Use Euler's method to solve the differential equation - Now, use Euler's method to solve the differential equation using a for loop. The MATLAB code is as follows: x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); %

Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end

Step 4: Plot the solution - Finally, plot the solution using the MATLAB command plot(x,y).

The complete MATLAB code is given below:

N = ...; %

Define N here y0 = 6.5; %

Define initial value of y here dx = ...; %

Define step size here x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); % Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end plot(x,y)

The plot of the solution will be displayed.

Learn more about differential equation visit:

brainly.com/question/32645495

#SPJ11

By applying the dynamic normalization approach, the new sample is added without requiring the re-normalization of the entire dataset.

To address the scenario where the dataset in data mining is a sample of a population and new samples with attribute values outside the range of the existing data may be added over time, we can use a dynamic normalization approach. This approach allows for the inclusion of new values without requiring the re-normalization of the entire dataset. Here is a description of the normalization approach that fulfills the given requirements:

1. Initialization:

  - Determine the maximum absolute value (max_abs) of the existing dataset. This can be calculated by taking the maximum absolute value across all attributes in the dataset.

2. Adding new values:

  - When a new sample is added to the dataset, compare the absolute values of its attributes with the current max_abs.

  - If the absolute value of any attribute in the new sample is greater than the current max_abs, update max_abs to the new maximum absolute value.

  - This ensures that the new sample is within the range -1 to 1, while preserving the normalization of the existing data.

3. Normalization calculation:

  - For each attribute value in the dataset, divide the value by max_abs. This will normalize the values within the range of -1 to 1.

  - If the original value was negative, the normalized value will retain its negative sign.

By following this dynamic normalization approach, we can accommodate new samples with attribute values outside the range of existing data while preserving the normalization of the old values.

Example:

Consider an existing dataset with the following attribute values:

[2, -4, 6, -8, 10]

1. Initialization:

  - The maximum absolute value (max_abs) in the existing dataset is 10.

2. Adding new values:

  - Suppose a new sample is added with attribute values [15, -12, 18, -20, 25].

  - Since 25 is greater than the current max_abs (10), update max_abs to 25.

3. Normalization calculation:

  - For the existing dataset, divide each attribute value by the updated max_abs (25).

    - Normalized dataset: [0.08, -0.16, 0.24, -0.32, 0.4]

  - For the new sample, divide each attribute value by the updated max_abs (25).

    - Normalized new sample: [0.6, -0.48, 0.72, -0.8, 1]

By applying this dynamic normalization approach, the new sample is added without requiring the re-normalization of the entire dataset. The resulting data maintains the range between -1 and 1 while accommodating new values outside the existing range.

Learn more about normalization here

https://brainly.com/question/33145407

#SPJ4

Answer:

[-5,4)

Step-by-step explanation:

Aidan just made one tiny mistake. They used a parenthese at the front which would mean that the -5 is not included in the interval. But the closed, colored-in dot on the graph means that the -5 IS supposed to be included. So the proper symbol to start the interval would be the square bracket to indicate the -5 is included. So it should be [-5, 4)

Answer: A

Step-by-step explanation:

Answer:

I could but can you please put down the problem.

Step-by-step explanation:

So, the sides of the triangle are approximately:

Side a ≈ 46.1 units

Side b = 42 units

Side c ≈ 43.4 units

And the angles of the triangle are:

Angle A ≈ 78 degrees

Angle B = 59 degrees

Angle C = 43 degree

To solve the triangle ABC with given angles and side, we can use the Law of Sines and Law of Cosines.

Given:

Angle B = 59 degrees

Angle C = 43 degrees

Side b = 42 units

Step 1: Find angle A

Since the sum of angles in a triangle is 180 degrees, we can find angle A:

Angle A = 180 - Angle B - Angle C

Angle A = 180 - 59 - 43

Angle A = 78 degrees

Step 2: Find side a using the Law of Sines

We can use the Law of Sines to find side a:

a / sin(A) = b / sin(B)

a / sin(78) = 42 / sin(59)

a = (42 * sin(78)) / sin(59)

a ≈ 46.1 units

Step 3: Find side c using the Law of Cosines

We can use the Law of Cosines to find side c:

c² = a² + b² - 2ab * cos(C)

c² = (46.1)² + (42)² - 2(46.1)(42) * cos(43)

c ≈ 43.4 units

So, the sides of the triangle are approximately:

Side a ≈ 46.1 units

Side b = 42 units

Side c ≈ 43.4 units

And the angles of the triangle are:

Angle A ≈ 78 degrees

Angle B = 59 degrees

Angle C = 43 degree

Learn more about triangle here:

https://brainly.com/question/2773823

#SPJ11

Aaron can make a triangular picture frame with 20 possible frames, as the third side can have 20 different integral lengths ranging from 19 cm to 38 cm.

To find the length of the third side of an isosceles triangle, we know that the two equal sides have lengths of 9 cm and 17 cm. Since it is an isosceles triangle, the length of the third side will also be equal to the other two sides. Therefore, the length of the third side is 9 cm.

In a triangle with integer side lengths, let's assume the second side has a length of x cm. Since one side is two times as long as the second side, the first side has a length of 2x cm. The third side has a length of 22 cm.

To find the greatest possible perimeter of the triangle, we want to maximize the sum of all three sides. Therefore, we want to choose the largest possible values for x and 2x that still satisfy the triangle inequality.

According to the triangle inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, we have the following inequality:

x + 2x > 22

Simplifying:

3x > 22

x > 7.333

Since x must be an integer, the largest possible value for x is 8.

Therefore, the greatest possible perimeter of the triangle is:

8 + 2(8) + 22 = 8 + 16 + 22 = 46 cm.

To form a triangle with sides of lengths 39 cm, 18 cm, and a third side of integral length, we need to ensure that the sum of any two sides is greater than the length of the third side, according to the triangle inequality.

Let's analyze the possible combinations of sides:

For the sides 39 cm and 18 cm:

The sum of these two sides is 39 + 18 = 57 cm, which is greater than the third side (since the sum must be greater than the third side). Therefore, this combination is valid.

For the sides 39 cm and the third side:

The sum of these two sides is 39 + third side, which must be greater than 18 cm for a valid triangle. Since the third side must have integral length, the possible lengths for the third side are from 19 cm to 38 cm (inclusive).

Therefore, Aaron can make a triangular picture frame with 20 possible frames, as the third side can have 20 different integral lengths ranging from 19 cm to 38 cm.

Learn more about integral here

https://brainly.com/question/30094386

#SPJ11

1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

Learn more about the wave function at

https://brainly.com/question/31744195

#SPJ11

Answer:

5x² + 9x - 10

Step-by-step explanation:

To completely simplify this equation, add all like terms.

3x² - 5 + 1 + 2x² + 9x - 6

= 5x² + 9x - 10

hope this helps :)

Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.

DIlations are defined by the follwing operation:

\(P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]\) (1)

Where:

If we know that \(O(x,y) = (1,1)\), \(k = 0.5\), \(J(x,y) = (3,1)\), \(K(x,y) = (5, -3)\), \(L(x,y) = (5,5)\) and \(M(x,y) = (3,7)\), then the coordinates of the new polygon are:

\(J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)]\)

\(J'(x,y) = (1,1)+0.5\cdot (2,0)\)

\(J'(x,y) = (1,1) +(1,0)\)

\(J'(x,y) = (2,1)\)

\(K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)]\)

\(K'(x,y) = (1,1) +0.5\cdot (4,-4)\)

\(K'(x,y) = (1,1) +(2,-2)\)

\(K'(x,y) = (3,-1)\)

\(L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)]\)

\(L'(x,y) = (1,1) + 0.5\cdot (4,4)\)

\(L'(x,y) = (1,1) + (2,2)\)

\(L'(x,y) = (3,3)\)

\(M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)]\)

\(M'(x,y) = (1,1) +0.5\cdot (2,6)\)

\(M'(x,y) = (1,1) +(1,3)\)

\(M'(x,y) = (2,4)\)

Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.

We kindly invite to check this question on dilations: https://brainly.com/question/13176891

Answer:

Step-by-step explanation:

O.    

\((-5)^2-(-6)^2\\25-36\\-11\)

P.

\(\frac{2}{(5)^2}\\ \frac{2}{25}\)

Q.

\(15-(-2)^4\\15-16\\-1\)

R.

\(2-12\\-10\)

Answer:

2x^2+7x-4

Step-by-step explanation:

(2x-1)(x+4)

\(=2x^{2} + 8x-x-4\\=2x^{2} +7x-4\)

Hope this helps!

Answer:

Step-by-step explanation:

2x\(2x² + 7x - 4.\)